Process Modeling and Deployment
Process Data Analysis - Insights/Inputs for Optimized Process Simulation
João Caldeira, jcppc@iscte-iul.pt, ISCTE-IUL1
Fernando Brito e Abreu, fba@iscte-iul.pt, ISCTE-IUL2
14 dezembro 2021
Environment Setup
Install R
Install R from here: https://cran.r-project.org/.
Install R Studio Desktop
Install R Studio Desktop from here: https://www.rstudio.com/products/rstudio/download/#download.
Install Required Libraries
install.packages("readxl")
install.packages("fitdistrplus")
install.packages("stats")
install.packages("actuar")
install.packages("vtable")
install.packages("data.table")
install.packages("dplyr")
install.packages("vioplot")
install.packages("bupaR")
install.packages("processanimateR")Load Required Libraries
library(readxl)
library(fitdistrplus)
library(stats)
library(actuar)
library(vtable)
library(data.table)
library(dplyr)
library(vioplot)
library(bupaR)
library(processanimateR)Dataset Preparation
Loading the Dataset
This filename should match your data location. The log file should have at least the columns named Case ID, Activity, Start Time, End Time.
dataset <- read_excel("C:/Users/Usuario/Desktop/Pastas/Escola/Universidade/Mestrado/1º Semestre/Modelação e Implementação de Processos/Trabalho Grupo/2ª Parte/G17.xlsx")
#colnames(dataset)[which(names(dataset) == "case")] <- "Case ID"
#colnames(dataset)[which(names(dataset) == "event")] <- "Activity"
#colnames(dataset)[which(names(dataset) == "resource")] <- "Resource"
colnames(dataset)[which(names(dataset) == "Start Timestamp")] <- "Start Time"
colnames(dataset)[which(names(dataset) == "Complete Timestamp")] <- "End Time"Formatting Date/Time columns
The Start Time and End Time columns should be formatted accordingly with the proper Date/Time mask present in the log file.
dataset[['Start Time']] <- as.POSIXct(dataset$`Start Time`, format = "%Y-%m-%d %H:%M:%S")
dataset[['End Time']] <- as.POSIXct(dataset$`End Time`, format = "%Y-%m-%d %H:%M:%S")Viewing the Dataset
dataset## # A tibble: 6,216 x 6
## `Case ID` Activity `Start Time` `End Time` Resource Role
## <dbl> <chr> <dttm> <dttm> <chr> <chr>
## 1 1 Create Pur~ 2010-12-31 23:00:00 2010-12-31 23:37:00 Kim Passa Requ~
## 2 1 Create Req~ 2011-01-01 04:37:00 2011-01-01 04:45:00 Kim Passa Requ~
## 3 1 Analyze Re~ 2011-01-01 05:41:00 2011-01-01 05:55:00 Karel de~ Purc~
## 4 1 Send Reque~ 2011-01-01 10:43:00 2011-01-01 11:09:00 Karel de~ Purc~
## 5 1 Create Quo~ 2011-01-01 11:32:00 2011-01-01 15:03:00 Magdalen~ Purc~
## 6 1 Analyze Qu~ 2011-01-01 21:44:00 2011-01-01 22:13:00 Immanuel~ Requ~
## 7 1 Choose bes~ 2011-01-01 22:13:00 2011-01-01 22:13:00 Tesca Lo~ Requ~
## 8 1 Settle con~ 2011-01-02 00:22:00 2011-01-02 08:20:00 Francois~ Purc~
## 9 1 Create Pur~ 2011-01-02 08:58:00 2011-01-02 09:10:00 Karel de~ Purc~
## 10 1 Confirm Pu~ 2011-01-02 13:09:00 2011-01-02 13:43:00 Sean Man~ Supp~
## # ... with 6,206 more rowsFiltering Only First Event of Each Case/Instance
#This is needed to compute the arrival time between instances/cases
filtered <- dataset[!duplicated(dataset$`Case ID`),]
filtered## # A tibble: 405 x 6
## `Case ID` Activity `Start Time` `End Time` Resource Role
## <dbl> <chr> <dttm> <dttm> <chr> <chr>
## 1 1 Create Pur~ 2010-12-31 23:00:00 2010-12-31 23:37:00 Kim Passa Requ~
## 2 4 Create Pur~ 2011-01-01 07:39:00 2011-01-01 08:00:00 Fjodor K~ Requ~
## 3 5 Create Pur~ 2011-01-01 08:49:00 2011-01-01 09:35:00 Esmana L~ Requ~
## 4 7 Create Pur~ 2011-01-01 13:05:00 2011-01-01 14:00:00 Esmana L~ Requ~
## 5 8 Create Pur~ 2011-01-01 13:27:00 2011-01-01 14:17:00 Fjodor K~ Requ~
## 6 10 Create Pur~ 2011-01-02 01:52:00 2011-01-02 02:43:00 Esmana L~ Requ~
## 7 12 Create Pur~ 2011-01-02 04:31:00 2011-01-02 04:41:00 Alberto ~ Requ~
## 8 13 Create Pur~ 2011-01-02 06:47:00 2011-01-02 07:06:00 Anna Kau~ Requ~
## 9 16 Create Pur~ 2011-01-02 18:25:00 2011-01-02 19:14:00 Esmana L~ Requ~
## 10 17 Create Pur~ 2011-01-02 18:32:00 2011-01-02 19:17:00 Anne Olw~ Requ~
## # ... with 395 more rowsOrdering by Start Date/Time
ordered <- filtered[order(as.POSIXct(filtered$`Start Time`), decreasing = FALSE),]
ordered## # A tibble: 405 x 6
## `Case ID` Activity `Start Time` `End Time` Resource Role
## <dbl> <chr> <dttm> <dttm> <chr> <chr>
## 1 1 Create Pur~ 2010-12-31 23:00:00 2010-12-31 23:37:00 Kim Passa Requ~
## 2 4 Create Pur~ 2011-01-01 07:39:00 2011-01-01 08:00:00 Fjodor K~ Requ~
## 3 5 Create Pur~ 2011-01-01 08:49:00 2011-01-01 09:35:00 Esmana L~ Requ~
## 4 7 Create Pur~ 2011-01-01 13:05:00 2011-01-01 14:00:00 Esmana L~ Requ~
## 5 8 Create Pur~ 2011-01-01 13:27:00 2011-01-01 14:17:00 Fjodor K~ Requ~
## 6 10 Create Pur~ 2011-01-02 01:52:00 2011-01-02 02:43:00 Esmana L~ Requ~
## 7 12 Create Pur~ 2011-01-02 04:31:00 2011-01-02 04:41:00 Alberto ~ Requ~
## 8 13 Create Pur~ 2011-01-02 06:47:00 2011-01-02 07:06:00 Anna Kau~ Requ~
## 9 16 Create Pur~ 2011-01-02 18:25:00 2011-01-02 19:14:00 Esmana L~ Requ~
## 10 17 Create Pur~ 2011-01-02 18:32:00 2011-01-02 19:17:00 Anne Olw~ Requ~
## # ... with 395 more rowsComputing Arrival Interval Between Cases/Instances
ordered <- data.table(ordered)
instances <- ordered[, Interval := difftime(as.POSIXct(ordered$`Start Time`), shift(as.POSIXct(ordered$`Start Time`), fill=ordered$`Start Time`[1L]), units="mins")]
instances <- instances[-c(1),]
instances## Case ID Activity Start Time
## 1: 4 Create Purchase Requisition 2011-01-01 07:39:00
## 2: 5 Create Purchase Requisition 2011-01-01 08:49:00
## 3: 7 Create Purchase Requisition 2011-01-01 13:05:00
## 4: 8 Create Purchase Requisition 2011-01-01 13:27:00
## 5: 10 Create Purchase Requisition 2011-01-02 01:52:00
## ---
## 400: 1917 Create Purchase Requisition 2011-10-08 20:07:00
## 401: 1920 Create Purchase Requisition 2011-10-09 03:59:00
## 402: 1929 Create Purchase Requisition 2011-10-09 22:27:00
## 403: 1938 Create Purchase Requisition 2011-10-11 13:48:00
## 404: 1949 Create Purchase Requisition 2011-10-13 05:27:00
## End Time Resource Role Interval
## 1: 2011-01-01 08:00:00 Fjodor Kowalski Requester 519 mins
## 2: 2011-01-01 09:35:00 Esmana Liubiata Requester 70 mins
## 3: 2011-01-01 14:00:00 Esmana Liubiata Requester 256 mins
## 4: 2011-01-01 14:17:00 Fjodor Kowalski Requester 22 mins
## 5: 2011-01-02 02:43:00 Esmana Liubiata Requester 745 mins
## ---
## 400: 2011-10-08 20:23:00 Miu Hanwan Requester 2247 mins
## 401: 2011-10-09 04:07:00 Penn Osterwalder Requester 472 mins
## 402: 2011-10-09 23:20:00 Elvira Lores Requester 1108 mins
## 403: 2011-10-11 14:08:00 Clement Duchot Requester 2361 mins
## 404: 2011-10-13 06:21:00 Tesca Lobes Requester 2379 minssummary(as.numeric(instances$Interval))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.0 216.5 498.5 1016.7 1109.2 12248.0sd(as.numeric(instances$Interval)) #Standard Deviation## [1] 1540.984var(as.numeric(instances$Interval)) #Variance## [1] 2374630Computing Activities Elapsed Time
dataset[['Elapsed Time']] <- as.difftime(difftime(dataset[['End Time']], dataset[['Start Time']], units="mins"))
model <- dataset
datasetActivities <- dataset
datasetActivities[,-c(1)][datasetActivities[,-c(1)]==0] <- NA
datasetActivities <- datasetActivities[complete.cases(datasetActivities),]
datasetActivities #[,c(1:6,7)] #Note: Viewing only some columns with changed order## # A tibble: 5,363 x 7
## `Case ID` Activity `Start Time` `End Time` Resource Role
## <dbl> <chr> <dttm> <dttm> <chr> <chr>
## 1 1 Create Pur~ 2010-12-31 23:00:00 2010-12-31 23:37:00 Kim Passa Requ~
## 2 1 Create Req~ 2011-01-01 04:37:00 2011-01-01 04:45:00 Kim Passa Requ~
## 3 1 Analyze Re~ 2011-01-01 05:41:00 2011-01-01 05:55:00 Karel de~ Purc~
## 4 1 Send Reque~ 2011-01-01 10:43:00 2011-01-01 11:09:00 Karel de~ Purc~
## 5 1 Create Quo~ 2011-01-01 11:32:00 2011-01-01 15:03:00 Magdalen~ Purc~
## 6 1 Analyze Qu~ 2011-01-01 21:44:00 2011-01-01 22:13:00 Immanuel~ Requ~
## 7 1 Settle con~ 2011-01-02 00:22:00 2011-01-02 08:20:00 Francois~ Purc~
## 8 1 Create Pur~ 2011-01-02 08:58:00 2011-01-02 09:10:00 Karel de~ Purc~
## 9 1 Confirm Pu~ 2011-01-02 13:09:00 2011-01-02 13:43:00 Sean Man~ Supp~
## 10 1 Deliver Go~ 2011-01-02 19:49:00 2011-01-03 02:37:00 Sean Man~ Supp~
## # ... with 5,353 more rows, and 1 more variable: Elapsed Time <drtn>summary(as.numeric(datasetActivities$`Elapsed Time`))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.0 6.0 14.0 130.2 31.0 2944.0sd(as.numeric(datasetActivities$`Elapsed Time`)) #Standard Deviation## [1] 387.0091var(as.numeric(datasetActivities$`Elapsed Time`)) #Variance## [1] 149776Computing Maximum and Minimum Hours of Work for Roles
datasetTemp <- dataset
datasetTemp[['Start Hours']] <- as.POSIXct(strftime(datasetTemp$`Start Time`, format="%H:%M:%S"), format = "%H:%M:%S")
datasetTemp[['End Hours']] <- as.POSIXct(strftime(datasetTemp$`End Time`, format="%H:%M:%S"), format = "%H:%M:%S")
labourHours <- datasetTemp %>%
group_by(Role) %>%
summarise(
"Minimum Hour" = min(`Start Hours`, na.rm = T),
"Maximum Hour" = max(`End Hours`, na.rm = T)
) %>%
arrange(Role)
labourHours[['Min. Hour']] <- format(labourHours$`Minimum Hour`, "%H:%M:%S")
labourHours[['Max. Hour']] <- format(labourHours$`Maximum Hour`, "%H:%M:%S")
labourHours[,-c(2,3)]## # A tibble: 5 x 3
## Role `Min. Hour` `Max. Hour`
## <chr> <chr> <chr>
## 1 Financial Manager 00:01:00 23:59:00
## 2 Purchasing Agent 00:01:00 23:59:00
## 3 Requester 00:00:00 23:56:00
## 4 Requester Manager 00:00:00 23:59:00
## 5 Supplier 00:02:00 23:59:00#par(mfrow=c(1,2))
proportion <- table(dataset$Role)/nrow(dataset)
boxplot(datasetTemp$`Start Time` ~ datasetTemp$Role, width=proportion, ylab="", xlab="Roles", las=1, cex.axis = 0.5) 
vioplot(as.numeric(datasetTemp$`Start Time`) ~ datasetTemp$Role, ylab="", xlab="Roles", las=1, cex.axis = 0.5, col = palette[2], horizontal = FALSE)
boxplot(datasetTemp$`End Time` ~ datasetTemp$Role, width=proportion, ylab="", xlab="Roles", las=1, cex.axis = 0.5)
vioplot(as.numeric(datasetTemp$`End Time`) ~ datasetTemp$Role, ylab="", xlab="Roles", las=1, cex.axis = 0.5, col = palette[2], horizontal = FALSE)
Dataset Evaluation
Instances Arrival Interval
Statistics
instances.interval <- as.numeric(instances$Interval)
summary(instances.interval)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.0 216.5 498.5 1016.7 1109.2 12248.0par(mfrow=c(2,2)) #Set a 2x2 matrix to plot 4 charts
hist(instances.interval, breaks = 20, main = "Histogram - Interval", xlab = "Interval")
hist(instances.interval, main = "Histogram - Interval (Zoom In)", breaks = 300, xlim = c(0,100), xlab = "Interval")
boxplot(instances.interval)
boxplot(instances.interval, ylim = c(0, 20)) #This is a scale reduced boxplot
Assess Distribution
descdist(instances.interval, discrete = FALSE)
## summary statistics
## ------
## min: 3 max: 12248
## median: 498.5
## mean: 1016.651
## estimated sd: 1540.984
## estimated skewness: 3.633647
## estimated kurtosis: 19.84013Fit/Compare the Distribution
# Distributions from "stats" package: norm,lnorm,exp,pois,cauchy,gamma,logis,nbinom,
# geom, beta,weibull
# Distributions from "actuar" package: invgamma,llogis,invweibull,pareto1,pareto
distribution <- fitdist(instances.interval, "norm")
plot(distribution)
Activities Elapsed Time
Statistics
activities.duration <- st(dataset, group = "Activity", vars=c("Elapsed Time"), group.long= TRUE, out = "return")
activities.duration## Variable N Mean
## 1 Activity: Amend Purchase Requisition
## 2 Elapsed Time 6 28.167
## 3
## 4 Activity: Amend Request for Quotation Requester
## 5 Elapsed Time 355 9.859
## 6
## 7 Activity: Amend Request for Quotation Requester Manager
## 8 Elapsed Time 30 19.1
## 9
## 10 Activity: Analyze Purchase Requisition
## 11 Elapsed Time 251 6.486
## 12
## 13 Activity: Analyze Quotation comparison Map
## 14 Elapsed Time 283 20.166
## 15
## 16 Activity: Analyze Request for Quotation
## 17 Elapsed Time 748 23.112
## 18
## 19 Activity: Approve Purchase Order for payment
## 20 Elapsed Time 283 1
## 21
## 22 Activity: Authorize Supplier's Invoice payment
## 23 Elapsed Time 283 0
## 24
## 25 Activity: Choose best option
## 26 Elapsed Time 283 0
## 27
## 28 Activity: Confirm Purchase Order
## 29 Elapsed Time 283 20.198
## 30
## 31 Activity: Create Purchase Order
## 32 Elapsed Time 283 9.622
## 33
## 34 Activity: Create Purchase Requisition
## 35 Elapsed Time 405 30.896
## 36
## 37 Activity: Create Quotation comparison Map
## 38 Elapsed Time 283 204.576
## 39
## 40 Activity: Create Request for Quotation Requester
## 41 Elapsed Time 160 9.7
## 42
## 43 Activity: Create Request for Quotation Requester Manager
## 44 Elapsed Time 203 1.99
## 45
## 46 Activity: Deliver Goods Services
## 47 Elapsed Time 283 1456.837
## 48
## 49 Activity: Pay invoice
## 50 Elapsed Time 283 9.29
## 51
## 52 Activity: Release Purchase Order
## 53 Elapsed Time 305 1
## 54
## 55 Activity: Release Supplier's Invoice
## 56 Elapsed Time 275 4.469
## 57
## 58 Activity: Send invoice
## 59 Elapsed Time 283 0
## 60
## 61 Activity: Send Request for Quotation to Supplier
## 62 Elapsed Time 283 23.155
## 63
## 64 Activity: Settle conditions with supplier
## 65 Elapsed Time 283 536.664
## 66
## 67 Activity: Settle dispute with supplier Financial Manager
## 68 Elapsed Time 60 23.233
## 69
## 70 Activity: Settle dispute with supplier Purchasing Agent
## 71 Elapsed Time 22 558.455
## Std. Dev. Min Pctl. 25 Pctl. 75 Max
## 1
## 2 3.971 23 25.25 31.75 32
## 3
## 4
## 5 2.978 5 7 13 15
## 6
## 7
## 8 4.887 12 15.25 24 27
## 9
## 10
## 11 3.977 4 5 7 65
## 12
## 13
## 14 7.955 6 14 27 34
## 15
## 16
## 17 8.51 0 18 29 50
## 18
## 19
## 20 0 1 1 1 1
## 21
## 22
## 23 0 0 0 0 0
## 24
## 25
## 26 0 0 0 0 0
## 27
## 28
## 29 9.998 4 13 28 94
## 30
## 31
## 32 2.151 6 8 12 13
## 33
## 34
## 35 15.207 5 17 45 57
## 36
## 37
## 38 90.55 38 136.5 279.5 365
## 39
## 40
## 41 2.298 4 8 11 16
## 42
## 43
## 44 0.704 1 1.5 2 3
## 45
## 46
## 47 796.874 183 776.5 2149.5 2944
## 48
## 49
## 50 3.078 4 7 12 15
## 51
## 52
## 53 0 1 1 1 1
## 54
## 55
## 56 1.461 2 3 6 7
## 57
## 58
## 59 0 0 0 0 0
## 60
## 61
## 62 7.83 1 18 27 88
## 63
## 64
## 65 190.877 238 365.5 710.5 879
## 66
## 67
## 68 6.573 13 17 29.25 34
## 69
## 70
## 71 24.861 523 540.5 567.5 620Assess Distribution
activities <- unique(dataset$Activity) # Get distinct activities names## 1 : Create Purchase Requisition | 2 : Create Request for Quotation Requester | 3 : Analyze Request for Quotation |
## 4 : Send Request for Quotation to Supplier | 5 : Create Quotation comparison Map | 6 : Analyze Quotation comparison Map |
## 7 : Choose best option | 8 : Settle conditions with supplier | 9 : Create Purchase Order |
## 10 : Confirm Purchase Order | 11 : Deliver Goods Services | 12 : Release Purchase Order |
## 13 : Approve Purchase Order for payment | 14 : Send invoice | 15 : Release Supplier's Invoice |
## 16 : Authorize Supplier's Invoice payment | 17 : Pay invoice | 18 : Analyze Purchase Requisition |
## 19 : Create Request for Quotation Requester Manager | 20 : Amend Request for Quotation Requester | 21 : Settle dispute with supplier Financial Manager |
## 22 : Amend Purchase Requisition | 23 : Settle dispute with supplier Purchasing Agent | 24 : Amend Request for Quotation Requester Manager |uniqueActivities = data.frame(ID=character(), Activity=character(), Value=integer())
#colnames(uniformActivities) <- c("ID", "Name", "Value")
for(i in 1:length(activities)) {
activity <- filter(dataset, Activity == activities[i])
if ( length(unique(activity$`Elapsed Time`)) == 1) { uniqueActivities <- rbind(uniqueActivities, data.frame(ID=i, Activity=activities[i],Value=unique(activity$`Elapsed Time`))); cat("\n", "Activity - ",i," : " ,activities[i],"with uniform value of : ", unique(activity$`Elapsed Time`),"\n"); next; }
descdist(as.numeric(activity$`Elapsed Time`), discrete = FALSE, graph = TRUE)
cat("\n", "Activity - ",i," : " , activities[i], "\n")
}
##
## Activity - 1 : Create Purchase Requisition
##
## Activity - 2 : Create Request for Quotation Requester
##
## Activity - 3 : Analyze Request for Quotation
##
## Activity - 4 : Send Request for Quotation to Supplier
##
## Activity - 5 : Create Quotation comparison Map
##
## Activity - 6 : Analyze Quotation comparison Map
##
## Activity - 7 : Choose best option with uniform value of : 0
##
## Activity - 8 : Settle conditions with supplier
##
## Activity - 9 : Create Purchase Order
##
## Activity - 10 : Confirm Purchase Order
##
## Activity - 11 : Deliver Goods Services
##
## Activity - 12 : Release Purchase Order with uniform value of : 1
##
## Activity - 13 : Approve Purchase Order for payment with uniform value of : 1
##
## Activity - 14 : Send invoice with uniform value of : 0
##
## Activity - 15 : Release Supplier's Invoice
##
## Activity - 16 : Authorize Supplier's Invoice payment with uniform value of : 0
##
## Activity - 17 : Pay invoice
##
## Activity - 18 : Analyze Purchase Requisition
##
## Activity - 19 : Create Request for Quotation Requester Manager
##
## Activity - 20 : Amend Request for Quotation Requester
##
## Activity - 21 : Settle dispute with supplier Financial Manager
##
## Activity - 22 : Amend Purchase Requisition
##
## Activity - 23 : Settle dispute with supplier Purchasing Agent
##
## Activity - 24 : Amend Request for Quotation Requester ManagerActivities with Unique Values
uniqueActivities## ID Activity Value
## 1 7 Choose best option 0
## 2 12 Release Purchase Order 1
## 3 13 Approve Purchase Order for payment 1
## 4 14 Send invoice 0
## 5 16 Authorize Supplier's Invoice payment 0Fit/Compare the Distribution
##
## Activity - Create Purchase Requisition# Distributions from "stats" package: norm,lnorm,exp,pois,cauchy,gamma,logis,nbinom,
# geom,beta,weibull
# Distributions from "actuar" package: invgamma,llogis,invweibull,pareto1,pareto
# The potential distribution was obtained in previous step. eg: norm, exp, etc
# Repeat below 3 lines per each activity name/index trying a corresponding distribution
activity <- filter(dataset, Activity == activities[1]) # Activity index 1
distribution <- fitdist(as.numeric(activity$`Elapsed Time`), "exp")
plot(distribution)
##
## Activity - Create Request for Quotation Requester# Distributions from "stats" package: norm,lnorm,exp,pois,cauchy,gamma,logis,nbinom,
# geom,beta,weibull
# Distributions from "actuar" package: invgamma,llogis,invweibull,pareto1,pareto
# The potential distribution was obtained in previous step. eg: norm, exp, etc
# Repeat below 3 lines per each activity name/index trying a corresponding distribution
activity <- filter(dataset, Activity == activities[4]) # Activity index 4
distribution <- fitdist(as.numeric(activity$`Elapsed Time`), "norm")
plot(distribution)
Appendix A
Probability Distributions (Examples)
Normal Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rnorm(observations, mean = 0, sd = 1)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.671300 -0.669355 -0.015493 -0.003188 0.697524 3.810277hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
Exponential Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rexp(observations, rate = 1)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000473 0.285721 0.701099 1.012070 1.379185 9.184451hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
Chi-Square Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rchisq(observations, df = 5)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.126 2.688 4.354 5.033 6.738 23.181hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
Logistic Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rlogis(observations)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -8.51509 -1.13675 -0.04549 -0.01524 1.16167 9.57546hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
Poisson Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rpois(observations, lambda = 15)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.00 12.00 15.00 15.03 18.00 35.00hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
t-Student Distribution
set.seed(1)
par(mfrow=plot.matrix)
sample.dataset <- rt(observations, df = 10)
summary(sample.dataset)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -4.89708 -0.68148 0.01846 0.02314 0.71075 5.43763hist(sample.dataset, main = "Histogram (Frequency)", breaks = bins.break, col = palette[1])
hist(sample.dataset, main = "Histogram (Density)", breaks = bins.break, col = palette[2], freq = FALSE)
lines(density(sample.dataset), lw = line.width, col = palette[3])
vioplot(sample.dataset, col = palette[2], horizontal = TRUE)
plot(density(sample.dataset), type="n", main ="")
polygon(density(sample.dataset), col=palette[4], border=palette[3])
rug(sample.dataset, col=palette[1])
Viewing the Process Model
include.in.render <- TRUE # Change this to FALSE to export to pdf (Knit to Pdf)
events <- model %>% #a data.frame with the information in the table above
mutate(Status = "complete",
Activity_Instance = 1:nrow(.)) %>%
eventlog(
case_id = "Case ID",
activity_id = "Activity",
activity_instance_id = "Activity_Instance",
lifecycle_id = "Status",
timestamp = "Start Time",
resource_id = "Resource"
)events %>% process_map(type = frequency("relative"), layout = layout_pm(fixed_positions = TRUE))events %>% process_map(performance(mean, "hours"))events %>% precedence_matrix(type = "absolute")## # A tibble: 35 x 3
## antecedent consequent n
## <fct> <fct> <int>
## 1 Amend Purchase Requisition Create Request for Quot~ 1
## 2 Analyze Purchase Requisition Amend Purchase Requisit~ 6
## 3 Amend Purchase Requisition Analyze Purchase Requis~ 5
## 4 Release Purchase Order Settle dispute with sup~ 22
## 5 Amend Request for Quotation Requester Manager Analyze Request for Quo~ 30
## 6 Analyze Request for Quotation Amend Request for Quota~ 355
## 7 Analyze Purchase Requisition Create Request for Quot~ 203
## 8 Settle dispute with supplier Financial Manager Authorize Supplier's In~ 60
## 9 Release Supplier's Invoice Settle dispute with sup~ 60
## 10 Analyze Request for Quotation Amend Request for Quota~ 30
## # ... with 25 more rowsevents %>% precedence_matrix(type = "absolute") %>% plot
#events %>% resource_map()
animate_process(events, mode = "relative", jitter = 10, legend = "color",
mapping = token_aes(size = token_scale(3), color = token_scale("Credit Request Cases/Instances", scale = "ordinal",
range = RColorBrewer::brewer.pal(12, "Paired"))))Invited Assistant Professor. https://ciencia.iscte-iul.pt/authors/joao-caldeira/cv↩︎
Associate Professor. https://ciencia.iscte-iul.pt/authors/fernando-brito-e-abreu/↩︎